Measuring an Event — Question 1

Question 1

A reception timestamp must be corrected for propagation

A fixed detector at the origin receives a flash at $t_R=12.0\,\mu\mathrm s$ from a known event position $x_E=900\,\mathrm m$. Use $c=3.00\times10^8\,\mathrm{m/s}$ and Einstein-synchronized laboratory clocks.

1. Assign the emission event its laboratory time.

2. Find the timing error if reception is mistaken for emission, and write the general correction for either sign of $x_E$.

Question 1 - Solution

A reception timestamp must be corrected for propagation

(a) Method and calculation

$$t_R=t_E+|x_E|/c.$$$$\boxed{t_E=12.0-3.0=9.0\,\mu\mathrm s}.$$

(b) Interpretation and further calculation

$$\boxed{t_R-t_E=3.0\,\mu\mathrm s}.$$$$\boxed{t_E=t_R-|x_E|/c}.$$

Physical check

An event coordinate is an assigned emission time, not the time its image reaches a distant observer.